"A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre."
This topic covers the properties of circles, how to find the circumference and area of a circle, and the different parts of a circle (such as chords, radii, and diameters).
Circle basics: Definitions of terms such as radius, diameter, chord, and tangent line.
Circumference: Formula for finding the distance around a circle.
Area: Formula for finding the amount of space inside a circle.
Arcs and central angles: Understanding how angles and arcs relate to each other in circles.
Sector: A portion of a circle, including the central angle and the corresponding arc.
Inscribed angles: Understanding angles that are formed by chords within a circle and how they relate to the arc they intercept.
Tangents and secants: Understanding lines that intersect a circle and their relationship with radius and diameter.
Intersecting chords: When two chords intersect within a circle, understanding the relationship between the segments they create.
Tangent-secant theorems: Relationship between the tangent and secant line's lengths in a circle.
Circle equations: The standard form, center-radius form, and general form of the equation of a circle.
Congruent circles: Circles that have the same radius.
Concentric circles: Circles that share the same center point, but have different radii.
Tangent circles: Circles that touch each other at exactly one point.
Intersecting circles: Circles that meet or cross each other at two points.
Secant circles: Circles that intersect each other at two points and have a line going through the center of each circle.
Perpendicular circles: Circles that intersect at right angles.
Chord: A straight line segment that connects two points on a circle.
Diameter: A straight line segment that passes through the center of a circle and touches two points on its circumference. It is twice the length of a radius.
Radius: A straight line segment that connects the center of a circle to any point on its circumference. It is half the length of a diameter.
Arc: A portion of the circumference of a circle.
"The distance between any point of the circle and the centre is called the radius."
"Usually, the radius is denoted r."
"A circle with r = 0 (a single point) is a degenerate case."
"A circle is an example of a simple closed curve that divides the plane into two regions: an interior and an exterior."
"In everyday use, the term 'circle' may be used interchangeably to refer to either the boundary of the figure or to the whole figure including its interior."
"In strict technical usage, the circle is only the boundary and the whole figure is called a disc."
"A circle may also be defined as a special kind of ellipse in which the two foci are coincident, the eccentricity is 0, and the semi-major and semi-minor axes are equal."
"A circle is the two-dimensional shape enclosing the most area per unit perimeter squared using calculus of variations."
"A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre."
"A circle is an example of a simple closed curve that divides the plane into two regions: an interior and an exterior."
"The distance between any point of the circle and the centre is called the radius."
"Usually, the radius is denoted r."
"A circle with r = 0 (a single point) is a degenerate case."
"In everyday use, the term 'circle' may be used interchangeably to refer to either the boundary of the figure or to the whole figure including its interior."
"In strict technical usage, the circle is only the boundary and the whole figure is called a disc."
"A circle may also be defined as a special kind of ellipse in which the two foci are coincident, the eccentricity is 0, and the semi-major and semi-minor axes are equal."
"A circle is the two-dimensional shape enclosing the most area per unit perimeter squared using calculus of variations."
"The circle is only the boundary."
"The whole figure is called a disc."